Asymptotics of the discrete log-concave maximum likelihood estimator and related applications
Balabdaoui, Fadoua; Jankowski, Hanna; Rufibach, Kaspar; Pavlides, Marios (2013), Asymptotics of the discrete log-concave maximum likelihood estimator and related applications, Journal of the Royal Statistical Society. Series B, Statistical Methodology, 75, 4, p. 769-790. http://dx.doi.org/10.1111/rssb.12011
TypeArticle accepté pour publication ou publié
External document linkhttp://arxiv.org/abs/1107.3904v4
Journal nameJournal of the Royal Statistical Society. Series B, Statistical Methodology
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Abstract (EN)The assumption of log-concavity is a flexible and appealing non-parametric shape constraint in distribution modelling. In this work, we study the log-concave maximum likelihood estimator of a probability mass function. We show that the maximum likelihood estimator is strongly consistent and we derive its pointwise asymptotic theory under both the well-specified and misspecified settings. Our asymptotic results are used to calculate confidence intervals for the true log-concave probability mass function. Both the maximum likelihood estimator and the associated confidence intervals may be easily computed by using the R package logcondiscr. We illustrate our theoretical results by using recent data from the H1N1 pandemic in Ontario, Canada.
Subjects / KeywordsConfidence interval; Discrete distribution; H1N1; Log-concavity; Misspecification; Non-parametric estimation; Shape constraints
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